Limit Theorems of Integrals with Respect to Vector Random Measures in Complete Paranormed Spaces

摘要

This paper studies random integral of the form ∫gd M, where f is a function taking value in a paranormed vector space X, and M is an independent scattered vector random measure. Random integrals of this type are a natural generalization of random series with paranormed space valued coefficients. Some limit theorems of integrals with respect to vector random measures are proved.